182 ON THE PASSAGE OF WAVES THKOTJGH
and when cos a = + 1,
-TT das
_ ,
= i + 7 + log -j-s
4
_ W L
512 f
16
6!=
429
the last term, deduced from A14, A16, being approximate.
For the values of -jr~^d^/dx we find from (91), (90), (92 kb = ^, 1, V2, 2:
TABLE V.
ft6 = 4 Jtb = l *& = ^/2 ft& = 2
cos a =0 eos2a=^ cos2a=l 0 -8448+0 -0974 i 0-8778 +0-0958 i 0 -9] 03 + 0 -0944 i 0-5615 + 0-3807 i 0-6998 + 0-3583?: 0-8353 + 0-3364?; 0-3123 + 0-7383 1 0-8587 + 0-5783^ 0-0102+1-38 0-518 +1-15 1-020 +0-8
These numbers correspond to the value of "W expressed in (82).
We have now, in pursuance of our method, to seek a second solution another form of W. The first which suggests itself with M* = 1 cloei answer the purpose. For (81) then gives as the leading term
_ <ty=r y-'n ]» = 25 dss |_(2/-7?)2 + <J-& fr-y2' ..................^
becoming infinite when tj ±b.
A like objection is encountered if ^ = 62 7/1 In this case
,_^) + 7?}Jl.
o
-- - = 2
dx The first part gives 4& simply when x becomes zero. And
f(y-<n)dy = - 2
8
sothat
(£
V
becoming infinite when ?;= + &.
So far as this difficulty is concerned we might take ^ = (62 -another form seems preferable, that is
.(9
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